So, I recently was able to get this issue solved (for me at least). I had to revisit this and although by no means scientific or totally exhaustive, here is what I noticed/did.
Assuming, the default Nintex task form properties controls are the same as the input controls, although they are disabled they seem to be submitting the data back causing my issue of it needing to be checked out. I have run into this before and seen it mentioned in other posts.
Previously, I deleted all of the item properties controls (leaving the labels) figuring nothing would be submitted if there were no property controls on the form at all. This still did not solve the issue, and I was still getting the error requiring it to be checked out. In a moment of clarity I noticed that the default Nintex task form also had layouts for smartphone, mobile, tablet. etc. and that they were linked to the original item property controls on the Desktop Layout. (I have only ever been concerned with and or manipulated the Desktop layouts so I never really paid much attention to the other layouts)
After deleting the property controls on the Desktop Layout, I deleted all of the other layouts except for Desktop, and now the form would work with the document checked in.
I reloaded the default form, left all the layouts but deleted the item property controls from ALL of the layouts and it worked with document checked in.
I left all of the layouts and deleted all of the item property controls except for just one on the smartphone layout, and back came the error.
So... although I was using the Desktop Layout, and had deleted the property controls (and even labels) on that layout, the item property controls on the other layout seem to be what was giving me grief. Perhapss some relationship remained to the controls on the other layouts even though they were deleted on the layout being used. In the end, I deleted the layouts I don't need, deleted all of the item property controls and replaced them with labels/reference data. I am happy I can get this to work, and get this info in my tool chest. But, is this the expected behavior? I would still consider myself a novice on this but it does seem a little counter-intuitive. Any thoughts?